Phase spectrum of the seismic wavelet is an important characteristic of seismic data. There are two major aspects of the seismic data phase control process. The first aspect is control of the seismic wavelet during intermediate processing steps. The second is phase control of the final seismic processing product, i.e., the seismic image. The first objective, wavelet phase control during intermediate processing steps, is important because some data processing methods assume particular phase properties of input data. If the input data deviates from the particular assumption, the processing method will produce a related error. Thus, careful phase control at this stage insures that input phase specification errors are reduced and the efficiency of intermediate processing steps with respect to the wavelet phase treatment is enhanced. The second objective, phase control of the seismic image, is important because detailed interpretation of seismic data may depend on the wavelet phase, and interpreters usually prefer a seismic wavelet with a particular phase property such as zero phase. A zero-phase wavelet in the seismic image means that the data have the highest possible resolution for a given amplitude spectrum. Such data are usually easier to interpret. It should be noted that both of the above-described phase control aspects are related in the sense that better phase control during intermediate processing results in better quality data before final conversion to (for example) zero phase and hence to a better quality final (zero-phase) product.
For example, there are typically modules in the processing stream that assume that the data being processed have a minimum phase spectrum. Nevertheless, the data will typically have a phase spectrum that is not minimum phase. (A concise discussion of wavelet phase may be found in the Encyclopedic Dictionary of Exploration Geophysics by R. E. Sheriff, 4th Ed. (2002) published by the Society of Exploration Geophysicists, in the definition of “phase characteristics.” See also the definition of “wavelet” as well as other terminology used herein.) Thus, error might be introduced by processing data that is not minimum phase.
One such module in a typical seismic data processing stream that assumes minimum phase property of the seismic wavelet is predictive deconvolution. Sheriff defines “deconvolution” as a “data processing technique applied to the seismic data for the purpose of improving the recognizability and resolution of reflected events.” The purpose of performing predictive deconvolution is to remove a predictable part of the seismic data defined in terms of a prediction distance, thus attenuating periodic multiples and, as an option, compressing the wavelet. This technique is discussed in the literature, for example by Robinson and Treitel in Geophysical Signal Analysis, Prentice-Hall (1980). In discussing the method of predictive deconvolution on page 267, the authors state, “it depends on the deterministic hypothesis that the basic seismic waveform associated with each of these events is minimum delay.” (See also page 29.)
Another module commonly used in seismic data processing that assumes minimum phase, or delay, is the receiver consistent deconvolution method. The purpose of this method is to correct the wavelet shape for receiver-related effects. A related but more general technique is surface consistent deconvolution which provides decomposition of the seismic wavelet into source, receiver, offset and common midpoint terms. Application of only one term from the solution, the receiver term, is equivalent to the result from receiver-consistent deconvolution.
Gibson and Larner pointed out the problem in 1984 in the context of vibroseis data processing (seismic data generated by a vibrator source). Predictive deconvolution is commonly applied to such data even though, as Gibson and Larner state, “this process involves a minimum phase assumption.” (“Predictive deconvolution and the zero-phase source,” Geophysics 49, 379-397 (1984)) As the authors note, vibroseis data will be much closer to zero phase. They disclose a solution in the form of correcting the phase of the original vibroseis data toward minimum phase before the deconvolution, and they illustrate the effectiveness of this approach. They use a phase correction filter based on a correlated vibroseis signature, the Klauder wavelet. However, their method of designing a minimum phase filter relies on statistical inferences from the seismic data rather than a deterministic approach such as is disclosed in the present invention. Moreover, Gibson and Larner do not account for phase distortions that can be caused by processing steps (e.g., frequency filters) that often precede predictive deconvolution in a typical processing stream. Hootman and Hart propose using the Gibson-Larner approach to compensate for phase differences arising when mixed sources (e.g., vibroseis and dynamite) are used in the same survey. (“The realities of processing mixed-source seismic surveys,” 68th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1436-1439 (1998)).
Connelly and Hart propose a method of making a phase correction post stack, after predictive deconvolution has been applied (pre-stack) to the data traces. (55th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 491-495 (1985)) For the most part, this method addresses only the second aspect of the phase control process, i.e., phase of the final seismic image. Furthermore, their post-stack approach relies on the commutative property of linear shift-invariant operations. Therefore, this requires all processes prior to the stack to be linear shift-invariant. Also, like Gibson and Larner, no attention is given to the problem of phase distortion from steps preceding predictive deconvolution.
Hart and Hootman point out that surface-consistent deconvolution is “subject to the same assumptions made when performing predictive deconvolution, which includes that there is a minimum-phase wavelet . . . ” (“Achieving consistent and stable phase with mixed-source surveys,” paper given at Sep. 5, 2000 Technical Luncheon, available at web site http://cseg.ca/luncheons/200009/) They propose using the approach disclosed in the Connelly and Hart paper cited above to correct this problem.
Martinez (U.S. Pat. No. 4,646,274) and Galbraith (U.S. Pat. No. 4,348,749) teach a method for using a vibrator source signature to correct for phase distortion introduced in standard processing of the data. They propose measuring the true ground force imparted to the earth by the vibrator to develop a phase correcting inverse filter. Like the method of Connelly and Hart, the filter is to be applied to the data after the processing.
Although minimum phase is preferred for processing steps such as predictive deconvolution, a zero-phase wavelet is preferred for the post-processing interpretation steps. (See Connelly and Hart, and also Sheriff and Geldart, Exploration Seismology, 2nd Ed., Cambridge University Press, 181 (1995). This is because zero-phase wavelets have the simplest shape and the highest peak for a given amplitude spectrum. Further, the peak occurs at the reflection time of the event. This alignment is important since the seismic wavelet generally broadens with increasing depth, with a zero-phase wavelet remaining symmetrical about the event time.
Robinson and Treitel make an argument at page 251 that reverberation pulse-train waveforms will arrive at the receiver exhibiting minimum delay, “or at least approximately so.” Nevertheless, the person skilled in the art of seismic processing will know that this assumption that the seismic data is minimum phase is often not accurate. The present invention provides a method of avoiding the error that can result from assuming the data have minimum phase spectrum.
Duren and Anderson disclose in U.S. Pat. No. 5,384,752 the following: “Because of the shortcomings of the statistical data analysis methods, deterministic methods are generally recognized as superior methods of analyzing seismic data. Deterministic methods involve directly measuring the waveform of the source pulse . . . [and using] a source pulse function that is based on the actual pulse instead of an estimated wavelet.” What is needed is a thorough, deterministic, pre-stack method of correcting wavelet phase spectrum to be consistent with assumptions in common data processing steps such as predictive deconvolution and also to shape the phase spectrum of the processed data for the following interpretation phase. The present invention satisfies these needs.